The Chewy Candy Company is test marketing a new candy bar in Seoul and Manila. In Seoul, the company sold 40 candy bars the firs
t month, and each month the cumulative total number of candy bars sold increases by 60. In Manila, the company sold 20 candy bars the first month, and the cumulative total number of candy bars sold increases by approximately 80% each month. In which month will the cumulative total number of candy bars sold in Manila first exceed the cumulative total in Seoul?
2 answers:
Looking at the image attached, we can see the assumed sales of the Chewy Candy Company for its new candy bar in Manila and Seoul. Setting up the given condition for separate branches, we clearly see that during the 6th month, the total sales in Manila first exceeded the cumulative total sales in Seoul.
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1. It is given that f(x) is 16 times the square root of x.
Putting that in mathematical terms we have,
f(x) = 16 *
also, y = f(x)
So, we have the function
y= 16
4. We need to solve the inequality equation : 4x + 2y ≤ 6
Let us take the equation,
4x+2y ≤ 6
2y ≤ 6-4x
y ≤
y ≤ 3-2x
So, any point (x,y) lies on the given inequality region, where y≤ 3-2x
5. Solving system of equations using addition method
Given:
-5x-y =38 ------> a
-6x-3y =60 -------> b
Divide the equation b by no. 3
(-6x-3y)/3 = 60/3
-2x-y = 20 -------> c
Subtracting equation c from a we have,
-5x-y - (-2x-y) = 38 - 20
-5x-y+2x+y = 18
-3x = 18
x = -6
Now, substituting the value of x in equation a, we get
-5(-6) - y =38
30-y =38
y= 30-38 = -8
y=-8
∴ x = -6 and y = -8
6. Finding composition of functions
Given : f(x) =15x + 7 ; g(x) = x² - 5x
To find : (f+g)(x)
(f+g) (x) = f(g(x))
So, replace the value of x in f(x) by g(x), where g(x)= x² - 5x
(f+g)(x) = 15(x²-5x) +7 =15x²-75x+7
∴ (f + g)(x) = 15x²-75x+7
7. System of 3 equations must be solved to find the solution
-8x-8y-5z=-6
7x-8y-9z =17
9x+2y+6z =-1
Solving by substitution method.
Isolate x from first equation :
x= (-6+8y+5z)/(-8)
Substitute this value of x in 2nd and 3rd equations.
Now, isolating y from the 2nd equation rewritten above, we have
y= -
Now substituting this value of y in the 3rd equation rewritten above, we have
Isolating z from above equation, we have
z = -2
Substitute z= -2 in the equation of y, we have
y= - = 1
y = 1
Substituting the value of y and z, in the equation of x, we have
x= (-6+8(1)+5(-2))/(-8) = 1
x = 1
∴ x=1 ; y = 1 ; z = -2
8. 5x ≤ 7
Solving the above equation, we have
x ≤ 7/5
Please see attachment for the graph.
9. The given function is : g(y) = -6
The domain is the set of values of y for which there can be a value of g(y).
Here g(y) can be real only if y is greater than or equal to 0.
∴ The domain of the given function is [0,∞) .
10. Given : y is a function of x.
Definition of function : A function is a relation that associates each element in the domain to one element of another set, the co-domain of the function.
∴ For each element x, in the domain, there is only one value of y in the range.
